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Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

3 May 2019

Papers citing "Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks"

50 / 60 papers shown

Title
A comprehensive analysis of PINNs: Variants, Applications, and Challenges Afila Ajithkumar Sophiya Akarsh K Nair S. Maleki S. Krishnababu PINN AI4CE 33 0 0 28 May 2025
Interpretable Machine Learning in Physics: A Review Sebastian Johann Wetzel Seungwoong Ha Raban Iten Miriam Klopotek Ziming Liu AI4CE 160 2 0 30 Mar 2025
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$ -sense Ariel Neufeld Tuan Anh Nguyen 83 0 0 30 Sep 2024
Dual Cone Gradient Descent for Training Physics-Informed Neural Networks Youngsik Hwang Dong-Young Lim AI4CE 117 3 0 27 Sep 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 97 7 0 08 May 2024
Architectural Strategies for the optimization of Physics-Informed Neural Networks Hemanth Saratchandran Shin-Fang Chng Simon Lucey AI4CE 73 0 0 05 Feb 2024
An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations Valentin Duruisseaux Amit Chakraborty AI4CE 74 1 0 04 Nov 2023
Adversarial Training for Physics-Informed Neural Networks Yao Li Shengzhu Shi Zhichang Guo Boying Wu AAML PINN 75 0 0 18 Oct 2023
Time integration schemes based on neural networks for solving partial differential equations on coarse grids Xinxin Yan Zhideng Zhou Xiaohan Cheng Xiaolei Yang AI4TS AI4CE 56 0 0 16 Oct 2023
Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schrödinger equations Jin Song Ilya Shenbin 125 27 0 29 Sep 2023
Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones Christian Berger Sadok Ben Toumia Zijian Zhou Zhenya Yan PINN 70 10 0 29 Sep 2023
Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmas J. Kumar D. Zarzoso V. Grandgirard Jana Ebert Stefan Kesselheim PINN 44 1 0 23 Aug 2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks Zheyuan Hu K. Shukla George Karniadakis Kenji Kawaguchi PINN AI4CE 174 103 0 23 Jul 2023
Efficient Error Certification for Physics-Informed Neural Networks Francisco Eiras Adel Bibi Rudy Bunel Krishnamurthy Dvijotham Philip Torr M. P. Kumar PINN 93 1 0 17 May 2023
Pseudo-Hamiltonian neural networks for learning partial differential equations Sølve Eidnes K. Lye 82 11 0 27 Apr 2023
$Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models$ Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models S. Shekarpaz Fanhai Zeng G. Karniadakis PINN 62 5 0 26 Apr 2023
Estimating Failure Probability with Neural Operator Hybrid Approach Mujing Li Yani Feng Guanjie Wang 16 2 0 24 Apr 2023
On the Limitations of Physics-informed Deep Learning: Illustrations Using First Order Hyperbolic Conservation Law-based Traffic Flow Models Archie J. Huang S. Agarwal AI4CE PINN 71 25 0 23 Feb 2023
Physics-Informed Koopman Network Yuying Liu A. Sholokhov Hassan Mansour S. Nabi AI4CE 84 3 0 17 Nov 2022
SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition Yihang Gao Ka Chun Cheung Michael K. Ng 63 16 0 16 Nov 2022
Physics-informed neural networks for operator equations with stochastic data Paul Escapil-Inchauspé G. A. Ruz 92 2 0 15 Nov 2022
Bayesian deep learning framework for uncertainty quantification in high dimensions Jeahan Jung Minseok Choi BDL UQCV 53 1 0 21 Oct 2022
Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling Giulia Bertaglia AI4CE 50 5 0 17 Oct 2022
Scaling transformation of the multimode nonlinear Schrödinger equation for physics-informed neural networks I. Chuprov D. Efremenko Jiexing Gao P. Anisimov V. Zemlyakov 49 0 0 29 Sep 2022
A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge Liron Simon Keren A. Liberzon Teddy Lazebnik 112 83 0 13 Sep 2022
Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition Yanqi Wu H. Aghamiry S. Operto Jianwei Ma 39 1 0 16 Aug 2022
PIAT: Physics Informed Adversarial Training for Solving Partial Differential Equations S. Shekarpaz Mohammad Azizmalayeri M. Rohban 41 4 0 14 Jul 2022
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread Giulia Bertaglia Chuan Lu L. Pareschi Xueyu Zhu AI4CE 50 20 0 25 Jun 2022
Scalable algorithms for physics-informed neural and graph networks K. Shukla Mengjia Xu N. Trask George Karniadakis PINN AI4CE 131 41 0 16 May 2022
Physics-informed neural networks for PDE-constrained optimization and control Jostein Barry-Straume A. Sarshar Andrey A. Popov Adrian Sandu PINN AI4CE 76 14 0 06 May 2022
RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations Shulan Qin Min Li Tao Xu Shaotong Dong 100 9 0 29 Apr 2022
AutoIP: A United Framework to Integrate Physics into Gaussian Processes D. Long Ziyi Wang Aditi S. Krishnapriyan Robert M. Kirby Shandian Zhe Michael W. Mahoney AI4CE 95 15 0 24 Feb 2022
Learning Stochastic Dynamics with Statistics-Informed Neural Network Yuanran Zhu Yunhao Tang Changho Kim 87 19 0 24 Feb 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 134 1,293 0 14 Jan 2022
Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes Zijian Zhou Li Wang Weifang Weng Zhenya Yan 63 19 0 18 Nov 2021
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems Jeremy Yu Lu Lu Xuhui Meng George Karniadakis PINN AI4CE 91 473 0 01 Nov 2021
Physics-informed Neural Network for Nonlinear Dynamics in Fiber Optics Xiaotian Jiang Danshi Wang Qirui Fan Min Zhang Chao Lu A. Lau AI4CE PINN 39 85 0 01 Sep 2021
Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series Annie E. Paine V. Elfving Oleksandr Kyriienko 62 23 0 06 Aug 2021
Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks Suryanarayana Maddu D. Sturm Christian L. Müller I. Sbalzarini AI4CE 87 83 0 02 Jul 2021
PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs Pu Ren Chengping Rao Yang Liu Jianxun Wang Hao Sun DiffM AI4CE 133 204 0 26 Jun 2021
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver Yuankai Teng Xiaoping Zhang Zhu Wang L. Ju 90 14 0 23 May 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 96 1,213 0 20 May 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 46 22 0 07 May 2021
Physics Informed Convex Artificial Neural Networks (PICANNs) for Optimal Transport based Density Estimation Amanpreet Singh Martin Bauer S. Joshi OT 32 1 0 02 Apr 2021
Physics-informed neural networks with hard constraints for inverse design Lu Lu R. Pestourie Wenjie Yao Zhicheng Wang F. Verdugo Steven G. Johnson PINN 102 522 0 09 Feb 2021
Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning Li Wang Zhenya Yan 115 48 0 12 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 117 153 0 22 Dec 2020
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 57 11 0 02 Dec 2020
A physics-informed operator regression framework for extracting data-driven continuum models Ravi G. Patel N. Trask M. Wood E. Cyr AI4CE 86 105 0 25 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 143 928 0 28 Jul 2020